Tetrapentagonal tiling

Tetrapentagonal tiling
Poincaré disk model of the hyperbolic plane
Type	Hyperbolic uniform tiling
Vertex configuration	(4.5)²
Schläfli symbol	r{5,4} or ${\begin{Bmatrix}5\\4\end{Bmatrix}}$ rr{5,5} or $r{\begin{Bmatrix}5\\5\end{Bmatrix}}$
Wythoff symbol	2 \| 5 4 5 5 \| 2
Coxeter diagram	or or
Symmetry group	[5,4], (542) [5,5], (552)
Dual	Order-5-4 rhombille tiling
Properties	Vertex-transitive edge-transitive

In geometry, the tetrapentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t₁{4,5} or r{4,5}.

Symmetry

A half symmetry [1⁺,4,5] = [5,5] construction exists, which can be seen as two colors of pentagons. This coloring can be called a rhombipentapentagonal tiling.

Dual tiling

The dual tiling is made of rhombic faces and has a face configuration V4.5.4.5:

Related polyhedra and tiling

Uniform pentagonal/square tilings v t e
Symmetry: [5,4], (*542)							[5,4]⁺, (542)	[5⁺,4], (5*2)	[5,4,1⁺], (*552)


{5,4}	t{5,4}	r{5,4}	2t{5,4}=t{4,5}	2r{5,4}={4,5}	rr{5,4}	tr{5,4}	sr{5,4}	s{5,4}	h{4,5}
Uniform duals


V5⁴	V4.10.10	V4.5.4.5	V5.8.8	V4⁵	V4.4.5.4	V4.8.10	V3.3.4.3.5	V3.3.5.3.5	V5⁵

Uniform pentapentagonal tilings v t e
Symmetry: $[5,5], (*552)$							$[5,5] +, (552)$
=	=	=	=	=	=	=	=

Order-5 pentagonal tiling ${5,5}$	Truncated order-5 pentagonal tiling $t{5,5}$	Order-4 pentagonal tiling $r{5,5}$	Truncated order-5 pentagonal tiling $2t{5,5} = t{5,5}$	Order-5 pentagonal tiling $2r{5,5} = {5,5}$	Tetrapentagonal tiling $rr{5,5}$	Truncated order-4 pentagonal tiling $tr{5,5}$	Snub pentapentagonal tiling $sr{5,5}$
Uniform duals


Order-5 pentagonal tiling $V5.5.5.5.5$	$V5.10.10$	Order-5 square tiling $V5.5.5.5$	$V5.10.10$	Order-5 pentagonal tiling $V5.5.5.5.5$	$V4.5.4.5$	$V4.10.10$	$V3.3.5.3.5$

*n42 symmetry mutations of quasiregular tilings: (4.n)² v t e
Symmetry *4n2 [n,4]	Spherical	Euclidean	Compact hyperbolic				Paracompact	Noncompact
Symmetry *4n2 [n,4]	*342 [3,4]	*442 [4,4]	*542 [5,4]	*642 [6,4]	*742 [7,4]	*842 [8,4]...	*∞42 [∞,4]	[ni,4]
Figures
Config.	(4.3)²	(4.4)²	(4.5)²	(4.6)²	(4.7)²	(4.8)²	(4.∞)²	(4.ni)²

*5n2 symmetry mutations of quasiregular tilings: (5.n)² v t e
Symmetry *5n2 [n,5]	Spherical	Hyperbolic					Paracompact	Noncompact
Symmetry *5n2 [n,5]	*352 [3,5]	*452 [4,5]	*552 [5,5]	*652 [6,5]	*752 [7,5]	*852 [8,5]...	*∞52 [∞,5]	[ni,5]
Figures
Config.	(5.3)²	(5.4)²	(5.5)²	(5.6)²	(5.7)²	(5.8)²	(5.∞)²	(5.ni)²
Rhombic figures
Config.	V(5.3)²	V(5.4)²	V(5.5)²	V(5.6)²	V(5.7)²	V(5.8)²	V(5.∞)²	V(5.∞)²

References

John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 19, The Hyperbolic Archimedean Tessellations)
"Chapter 10: Regular honeycombs in hyperbolic space". The Beauty of Geometry: Twelve Essays. Dover Publications. 1999. ISBN 0-486-40919-8. LCCN 99035678.

External links

Tessellation

Periodic
Pythagorean Rhombille Schwarz triangle Rectangle Domino Uniform tiling and honeycomb Coloring Convex Kisrhombille Wallpaper group Wythoff

Aperiodic
Ammann–Beenker Aperiodic set of prototiles List Einstein problem Socolar–Taylor Gilbert Penrose Pinwheel Quaquaversal Rep-tile and Self-tiling Sphinx Socolar Truchet

Other
Anisohedral and Isohedral Architectonic and catoptric Circle Limit III Computer graphics Honeycomb Isotoxal List Packing Pentagonal Problems Domino Wang Heesch's Squaring Dividing a square into similar rectangles Prototile Conway criterion Girih Regular Division of the Plane Regular grid Substitution Voronoi Voderberg

By vertex type

Spherical	2ⁿ 3³.n V3³.n 4².n V4².n
Regular	2^∞ 3⁶ 4⁴ 6³
Semi- regular	3².4.3.4 V3².4.3.4 3³.4² 3³.∞ 3⁴.6 V3⁴.6 3.4.6.4 (3.6)² 3.12² 4².∞ 4.6.12 4.8²
Hyper- bolic	3².4.3.5 3².4.3.6 3².4.3.7 3².4.3.8 3².4.3.∞ 3².5.3.5 3².5.3.6 3².6.3.6 3².6.3.8 3².7.3.7 3².8.3.8 3³.4.3.4 3².∞.3.∞ 3⁴.7 3⁴.8 3⁴.∞ 3⁵.4 3⁷ 3⁸ 3^∞ (3.4)³ (3.4)⁴ 3.4.6².4 3.4.7.4 3.4.8.4 3.4.∞.4 3.6.4.6 (3.7)² (3.8)² 3.14² 3.16² 3.∞² 4².5.4 4².6.4 4².7.4 4².8.4 4².∞.4 4⁵ 4⁶ 4⁷ 4⁸ 4^∞ (4.5)² (4.6)² 4.6.12 4.6.14 V4.6.14 4.6.16 V4.6.16 4.6.∞ (4.7)² (4.8)² 4.8.10 V4.8.10 4.8.12 4.8.14 4.8.16 4.8.∞ 4.10² 4.10.12 4.12² 4.12.16 4.14² 4.16² 4.∞² 5⁴ 5⁵ 5⁶ 5^∞ 5.4.6.4 (5.6)² 5.8² 5.10² 5.12² 6⁴ 6⁵ 6⁶ 6⁸ 6.4.8.4 (6.8)² 6.8² 6.10² 6.12² 6.16² 7³ 7⁴ 7⁷ 7.6² 7.8² 7.14² 8³ 8⁴ 8⁶ 8⁸ 8.6² 8.12² 8.16² ∞³ ∞⁴ ∞⁵ ∞^∞ ∞.6² ∞.8²

This hyperbolic geometry-related article is a stub. You can help Wikipedia by expanding it.

Read other articles:

Nugroho Suksmanto

Artikel ini sebatang kara, artinya tidak ada artikel lain yang memiliki pranala balik ke halaman ini.Bantulah menambah pranala ke artikel ini dari artikel yang berhubungan atau coba peralatan pencari pranala.Tag ini diberikan pada Desember 2022. Artikel ini sebatang kara, artinya tidak ada artikel lain yang memiliki pranala balik ke halaman ini.Bantulah menambah pranala ke artikel ini dari artikel yang berhubungan atau coba peralatan pencari pranala.Tag ini diberikan pada Oktober 2022. Nugroh...

Celurut Iran

Artikel ini sebatang kara, artinya tidak ada artikel lain yang memiliki pranala balik ke halaman ini.Bantulah menambah pranala ke artikel ini dari artikel yang berhubungan atau coba peralatan pencari pranala.Tag ini diberikan pada Januari 2023. Celurut Iran Crocidura susiana Status konservasiGentingIUCN5618 TaksonomiKerajaanAnimaliaFilumChordataKelasMammaliaOrdoEulipotyphlaFamiliSoricidaeGenusCrociduraSpesiesCrocidura susiana DistribusiPersebaran celurut Iran lbs Celurut Iran (Crocidura susia...

Thérésa Tallien

Spanish-born French noblewoman and socialite (1773–1835) Thérésa TallienPortrait of Madame Tallien, by Jean-Bernard Duvivier, 1806BornJuana María Ignacia Teresa de Cabarrús y Galabert31 July 1773 (1773-07-31)Carabanchel Alto, Madrid, Spain[1]Died15 January 1835 (1835-01-16) (aged 61)Chimay, Hainaut, BelgiumKnown forLiaisons with high-profile men - and the role as symbol of the end of terror in France (Notre Dame du Thermidor)Spouse(s)1 Marquis de Fontenay (annulle...

Ubi jalar

Ubi jalar Umbi Bunga Klasifikasi ilmiah Domain: Eukaryota Kerajaan: Plantae (tanpa takson): Tracheophyta (tanpa takson): Angiospermae (tanpa takson): Eudikotil (tanpa takson): Asteridae Ordo: Solanales Famili: Convolvulaceae Genus: Ipomoea Spesies: Ipomoea batatas(L.) Lam. Ubi jalar, ubi rambat, ubi manis, ubi jawa, ubi jenderal, petatas, ketela , atau ketela rambat (Ipomoea batatas) adalah sejenis tanaman budidaya. Bagian yang dimanfaatkan adalah akarnya yang membentuk umbi dengan kadar giz...

Giuseppe venduto dai suoi fratelli

Disambiguazione – Se stai cercando altri significati, vedi Giuseppe venduto dai fratelli. Giuseppe condotto dai mercanti in un quadro del pittore russo Konstantin Dmitrievič Flavickij (1855). La vendita di Giuseppe (in ebraico מכירת יוסף‎?, mekhirá Yoséf), o Giuseppe venduto dai suoi fratelli, è un episodio biblico tratto dal libro della Genesi. Indice 1 Tema 2 Racconto 3 Note 3.1 Riferimenti 4 Bibliografia 5 Altri progetti Tema Stabilitosi finalmente nella terra de...

Čop Street

Street in Ljubljana, Slovenia Čop StreetČop Street, as seen from Prešeren SquareNative nameČopova ulica (Slovene)Former name(s)Elephant StreetSlonova ulicaPrešeren StreetPrešernova ulicaLength205 m (673 ft)LocationCenter District, Ljubljana, SloveniaCoordinates46°03′07″N 14°30′16″E / 46.05191°N 14.50448°E / 46.05191; 14.50448Northwest endSlovene Street(Slovenska cesta)Southeast endPrešeren Square(Prešernov trg) Čop Street (...

Adrienne Dore

Artikel ini sebatang kara, artinya tidak ada artikel lain yang memiliki pranala balik ke halaman ini.Bantulah menambah pranala ke artikel ini dari artikel yang berhubungan atau coba peralatan pencari pranala.Tag ini diberikan pada November 2022. Adrienne DoreDore dalam sebuah foto Elmer Fryer, 1932LahirElizabeth Himmelsbach(1907-05-22)22 Mei 1907Coeur d'Alene, Idaho, Amerika SerikatMeninggal26 November 1992(1992-11-26) (umur 85)Los Angeles, California, Amerika SerikatNama lainAdrien...

Courage Compétition

Oreca-Courage LC70 Courage Compétition adalah sebuah tim balap dan perusahaan pembangun sasis yang sekarang dimiliki oleh Oreca, yang berbasis di Le Mans, Prancis dekat dengan Circuit de la Sarthe. Tim ini didirikan oleh Yves Courage, seorang pembalap asal Prancis yang mengikuti event hillclimb sebelum pendirian perusahaan. Setelah pembelian Courage oleh Oreca pada tahun 2007, Yves Courage mendirikan kembali perusahaannya dengan nama Courage Technology pada tahun 2010, berusaha untuk mengemb...

Jumeirah Beach Hotel

This article may rely excessively on sources too closely associated with the subject, potentially preventing the article from being verifiable and neutral. Please help improve it by replacing them with more appropriate citations to reliable, independent, third-party sources. (November 2013) (Learn how and when to remove this message) Building in Dubai, United Arab EmiratesJumeirah Beach Hotel جميرا بيتش هوتيلGeneral informationLocationDubai, United Arab EmiratesCoordinates25°08...

Blackcurrant production in the United States

Agricultural production Blackcurrant fruit Blackcurrant production in the United States is relatively limited. The blackcurrant (Ribes nigrum) was introduced by English settlers at the Massachusetts Bay Colony in 1629 and was cultivated on some scale, particularly in New York. The plant acts as a host for the white pine blister rust that threatened the timber industry. In 1911, the federal government banned the cultivation, sale, and transport of blackcurrants to protect the white pine. Gover...

Punch (magazine)

British weekly magazine of humour and satire This article is about the British magazine. For other publications, see Punch § Periodicals. Punch, or The London CharivariCover of the first Punch, or The London Charivari, depicts Punch hanging a caricatured Devil, 1841 (see gallery below for enlarged detail)CategoriesPolitics, culture, humour and satireFrequencyWeeklyFounderHenry MayhewEbenezer LandellsFounded1841First issue17 July 1841Final issue2002CountryUnited KingdomBased inLondonLanguageE...

David Stuart (brigadier general)

Union Army officer and politician For other people with the same name, see David Stuart (disambiguation). David StuartCol. David StuartBorn(1816-03-12)March 12, 1816Brooklyn, New YorkDiedSeptember 11, 1868(1868-09-11) (aged 52)Detroit, MichiganBuriedElmwood Cemetery, Detroit, MichiganAllegianceUnited States of AmericaUnionService/branchUnited States ArmyUnion ArmyRank Brigadier General (rejected by United States Senate)Battles/warsAmerican Civil War Battle of Shiloh Siege of Corinth Batt...

England national amateur football team

Association football team England AmateursAssociationThe Football AssociationMost capsRod Haider (65)Top scorerVivian Woodward (45)FIFA codeENG Home colours Away colours First international England Amateurs 12–0 Germany (London, England; 21 September 1901)[1][a]Biggest win France 0–15 England Amateurs (Paris, France; 1 November 1906)[2]: 5–6, 16 Biggest defeat Ireland Amateurs 5–1 England Amateurs (Belfast, Ir...

Grand Prix F1 Tiongkok 2005

Grand Prix Tiongkok 2005 Lomba ke-19 dari 19 dalam Formula Satu musim 2005 Detail perlombaanTanggal 16 Oktober 2005Nama resmi II Sinopec Chinese Grand PrixLokasi Shanghai International CircuitShanghai, TiongkokSirkuit Fasilitas Balap PermanenPanjang sirkuit 5.451 km (3.387 mi)Jarak tempuh 56 putaran, 305.066 km (189.559 mi)Cuaca CerahPosisi polePembalap Fernando Alonso RenaultWaktu 1.34.080Putaran tercepatPembalap Kimi Räikkönen McLaren-MercedesWaktu 1.33.242 putaran ke-56PodiumPertama Fern...

Dewan Perwakilan Rakyat Daerah Kabupaten Solok Selatan

Dewan Perwakilan Rakyat Daerah Kabupaten Solok SelatanDewan Perwakilan Rakyat Kabupaten Solok Selatan 2019-2024JenisJenisUnikameral SejarahSesi baru dimulai14 Agustus 2019PimpinanKetuaZigo Rolanda, S.E. (Golkar) sejak 25 September 2019 Wakil Ketua IYendri Susanto (PAN) sejak 2 Desember 2021 Wakil Ketua IIArmen Syahjohan, S.IP. (Gerindra) sejak 25 September 2019 KomposisiAnggota25Partai & kursi NasDem (3) PKB (2) Demokrat (2) PAN ...

August Schell Brewing Company

August Schell Brewing CompanyLocation1860 Schell Rd[1]New Ulm, MinnesotaUnited StatesOpened1860Annual production volume145,000 US beer barrels (170,000 hL)[2]Active beers Name Type Schell's Deer Brand Pre-Prohibition American lager Schell's Light America Light lager Schell's Amber Red American lager Schell's Firebrick Vienna-Style Amber lager Schell's Cream Ale Cream Ale Schell's IPA India Pale Ale Schell's Dark American dark lager Schell's LoCal Twist Wheat Beer Grain Be...

Massacre of 1391

Antisemitic violence in the Iberian Peninsula peaking in 1391 massacreMassacre of 1391Part of Antisemitism in EuropeSlaughter of Jews in Barcelona in 1391 (José Segrelles, c. 1910)LocationCrown of Castile, Crown of AragonDate1391TargetJewsAttack typePogromMotiveAntisemitism The Massacre of 1391, also known as the pogroms of 1391, refers to a murderous wave of mass violence committed against the Jews of Spain by the Catholic populace in the kingdoms of Castile and Aragon, both in present-day ...

レニウム

タングステン ← レニウム → オスミウム Tc↑Re↓Bh 75Re 周期表外見銀灰色一般特性名称, 記号, 番号レニウム, Re, 75 分類遷移金属族, 周期, ブロック 7, 6, d 原子量 186.207 電子配置 [Xe] 4f14 5d5 6s2 電子殻 2, 8, 18, 32, 13, 2（画像）物理特性相固体密度（室温付近） 21.02 g/cm3 融点での液体密度 18.9 g/cm3 融点 3459 K, 3186 °C, 5767 °F 沸点 5870 K, 5597 °C, 10106 ...

Composé polyédrique

Un composé polyédrique est un polyèdre qui est lui-même composé de plusieurs autres polyèdres partageant un centre commun, l'analogue tridimensionnel des composés polygonaux (en) tels que l'hexagramme. Les sommets voisins d'un composé peuvent être connectés pour former un polyèdre convexe appelé l'enveloppe convexe. Le composé est un facettage de l'enveloppe convexe. Un autre polyèdre convexe est formé par le petit espace central commun à tous les membres du composé. Ce ...

Homi K. Bhabha

Indian critical theorist (born 1949) This article is about the critical theorist. For the physicist, see Homi J. Bhabha. Homi K. BhabhaBorn (1949-11-01) 1 November 1949 (age 74)Bombay, Province of Bombay, Dominion of India(now Mumbai, Maharashtra, India)SpouseJacqueline BhabhaChildren3Academic backgroundAlma materSt. Mary's School, MumbaiUniversity of Mumbai Christ Church, OxfordAcademic workSchool or traditionPost-colonial theoryPost-structuralismInstitutionsUniversity of SussexPrinceto...

PROFILPELAJAR.COM